With the advent of agentic AI, Software Engineering is transforming to a new era dubbed Software Engineering 3.0. Software project management (SPM) must also evolve with such transformations to boost successful project completion, while keeping humans at the heart of it. Building on our preliminary ideas of “agentic SPM”, and supporting literature, we present our vision of an “Agentic Project Manager (PM)” as a multi-agent system for SPM 3.0. They will work like a “junior project manager”, or an “intern project manager” collaboratively with software teams. We introduce four working modes, with varying autonomy levels to choose from, based on task complexity and risk levels. This addresses concerns with ethics, accountability, and trust related to agentic PMs. We also share insights on human PM role evolution and new skill requirements as a “strategic leader” and a “coach” for humans and agents. While creating the foundation for agentic SPM research, we present a research agenda for the wider research community.